Math 021 Formulas and Concepts Rectangular Box Surface Area SA 2Lw 2Lh 2hw Cone Volume V 1 3 r2 h Cylinder Surface Area SA 2 r2 2 r h Triangular Field A B C Formula A B C 180 Sale Formula Total Value Unit Price Number Distance Formula Distance rate time Investing Banking Formula I P R T I simple interest earned on investment or paid on loan P Principle amount invested or borrowed R interest rate in decimal form T Time invested ITotal PR PRT ITotal dec of 1 x dec of 2 P x x 1st amount invested Concentration Formula Concentration Amount of component Amount of component Concentration Amount of mixture amt 1 amt 2 amt T Linear inequality in one variable Can be written in the form ax b c Set Builder Notation Interval notation Contradiction Identity Resulting values on both sides are the same Example 2x 2x All real numbers or x x is a real number Equation can never be true No solution Example x x 1 Amount of mixture Example x x 5 Example 2 5 a bx c A B set of all things either A or B A B set of all things in both A and B True for some values of the equation but not others Conditional ABSOLUTE VALUE EQUATIONS AND INEQUALITY PROPERTIES Let u be an algebraic expression and let c be a real number such that c 0 then 1 u c is equivalent to u c or u c 2 u c is equivalent to c u c 3 u c is equivalent to u c or u c Special Cases c 0 u 0 no solution u 0 u 0 u 0 u 0 u 0 u 0 R Union Intersection 3 Part Inequality Standard Form Dependent variable variable we solve for value depends on the remaining variables independent variables Relation set of ordered pairs Domain set of all values for the independent variable Range set of all values for the dependent variable Function relation where value in domain corresponds with exactly 1 value in the range Vertical line test Function notation f x 2x 3 Linear Equation in 2 variables Linear function X and Y Intercepts To find x intercepts let y 0 Use to determine if a graph is a function Not a function if a vertical line can pass 2 points Standard form Ax By C f x ax b Ex Equations and graphs Shows the connection between a set of values for the independent variable domain and dependent variable range Same slope different y intercepts To find y intercepts let x 0 Slope Slope m m rise run change y change x y2 y1 x2 x1 Horizontal line has 0 slope Horizontal Line y b Vertical Line x a undefined slope Point Slope Form equation of a line y y1 m x x1 Slope Intercept Form equation of a line y mx b m is slope and b is y intercept 0 b Standard Form of equation of a line Ax By C Parallel Lines Perpindicular lines m1 m2 1 or slope lines are negative reciprocals of each other m1 1 m2 Same or different y intercepts Intersecting but not perpendicular Coinciding Lines System of Linear Equations in 2 variables Consistent Independent Inconsistent Independent Consistent dependent Monomial expression containing 1 term Binomial expression containing 2 terms No solution 2 lines have no common points Same slope but different y intercepts Same slope same y intercept Infinitely many solutions Same slope same y intercept Different slopes but m1 m2 1 1 Solution Trinomial expression containing 3 terms Multinomial expression containing more than 1 term Coefficient of the monomial The constant factor of the monomial If there is no constant factor then the coefficient is understood to be 1 Degree The power to which the variable is raised If the term or monomial contains several variables then the degree is the sum of the powers of all the variables The degree of a polynomial is the degree of the term with the highest degree Difference of two Squares a b a b a2 b2 a b a b Squaring a Binomial a b 2 a b 2 a2 2ab b2 Squaring a Binomial a b 2 a b 2 a2 2ab b2 Cubing a Binomial a b 3 a b 3 a3 3a2b 3ab2 b3 Cubing a Binomial a b 3 a b 3 a3 3a2b 3ab2 b3 Sum and Difference of two Cubes a3 b3 a b a2 ab b2 a3 b3 a b a2 ab b2 Rational Expression Algebraic Expression with form P Q P and Q are polynomials such that Q 0 Domain of a rational function Set of all real numbers except those that make the denominator equal 0 Equation that equals negative one A B B A Expression Factored Version a2 2ab b2 a2 2ab b2 a3 3a2b 3ab2 b3 a3 3a2b 3ab2 b3 a b a2 ab b2 a b a2 ab b2 a b a b a b 2 a b 2 a b 3 a b 3 a3 b3 a3 b3 a2 b2 Rate of work The number of jobs that can be completed in a given unit of time If one job can be completed in units of time then the rate of work is given by 1 t Rate for two workers 1 t1 1 t2 1 t Here and are the individual times to complete one job and is the time to complete the job when working together Definition Principal and Negative Square Roots A non negative real number b is the principal square root of a non negative real number a denoted as b a if b2 a A negative real number b is the negative square root of a non negative real number a denoted as b a if b2 a a2 a Simplifying Radical Expressions of the Form n an If n is an integer such that n 2 and a is a real number then n an a if n is odd n an a if n is even Domain of a Radical Function If the index of a radical function is even the radicand must be greater than or equal to zero If the index of a radical function is odd the radicand can be any real number Rationalizing a Denominator with One Term To rationalize a denominator with a single radical of index n multiply the numerator and denominator by a radical of index n so that the radicand in the denominator is a perfect nth power Rationalizing a Denominator with Two Terms To rationalize a denominator with two terms involving one or more square roots multiply the numerator and denominator by the conjugate of the denominator Imaginary Unit i i 1 i2 1 Simplifying i divide n by 4 Remainder i n 0 1 1 i 2 1 3 i Complex Numbers The set of all numbers of the form a bi a 1 a i a Square Root Property U is an algebraic Expression K Real number can be U2 K U K or U K Every quadratic equation can be written in the form …